Related papers: A New Modified Newton-Type Iteration Method for So…

In this paper, we propose a distributed Newton method for consensus optimization. Our approach outperforms state-of-the-art methods, including ADMM. The key idea is to exploit the sparsity of the dual Hessian and recast the computation of…

Randomized Kaczmarz (RK), Motzkin Method (MM) and Sampling Kaczmarz Motzkin (SKM) algorithms are commonly used iterative techniques for solving a system of linear inequalities (i.e., $Ax \leq b$). As linear systems of equations represent a…

Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This work develops an alternative…

We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…

Physics-Informed Neural Networks (PINNs) have gained popularity in solving nonlinear partial differential equations (PDEs) via integrating physical laws into the training of neural networks, making them superior in many scientific and…

The random feature method (RFM), a mesh-free machine learning-based framework, has emerged as a promising alternative for solving PDEs on complex domains. However, for large three-dimensional nonlinear problems, attaining high accuracy…

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…

This article introduces an iterative method for solving nonsingular non-Hermitian positive semidefinite systems of linear equations. To construct the iteration process, the coefficient matrix is split into two non-Hermitian positive…

Stein variational gradient descent (SVGD) is a general-purpose optimization-based sampling algorithm that has recently exploded in popularity, but is limited by two issues: it is known to produce biased samples, and it can be slow to…

In this paper, we present a new modified Newton method a use of Haar wavelet formula for solving non-linear equations. This new method do not require the use of the second-order derivative. It is shown that the new method has third-order of…

In the present paper, in order to fnd a singularity of a vector field defined on Riemannian manifolds, we present a new globalization strategy of Newton method and establish its global convergence with superlinear rate. In particular, this…

We illustrate the stochastic method for solving the Schwinger-Dyson equations in large-N quantum field theories described in ArXiv:1009.4033 on the example of the Gross-Witten unitary matrix model. In the strong-coupling limit, this method…

The linearly constrained convex composite programming problems whose objective function contains two blocks with each block being the form of nonsmooth+smooth arises frequently in multiple fields of applications. If both of the smooth terms…

Unconstrained convex optimization problems have enormous applications in various field of science and engineering. Different iterative methods are available in literature to solve such problem, and Newton method is among the oldest and…

Newton's method has been an important approach for solving variational inequalities, quasi-Newton method is a good alternative choice to save computational cost. In this paper, we propose a new method for solving monotone variational…

We present a sparse Gauss-Newton solver for accelerated sensitivity analysis with applications to a wide range of equilibrium-constrained optimization problems. Dense Gauss-Newton solvers have shown promising convergence rates for inverse…

In this article we investigate a finite element formulation of strongly monotone quasi-linear elliptic PDEs in the context of fixed-point iterations. As opposed to Newton's method, which requires information from the previous iteration in…

We study numerical methods for the generalized Langevin equation (GLE) with a positive Prony series memory kernel, in which case the GLE can be written in an extended variable Markovian formalism. We propose a new splitting method that is…

In 1-bit matrix completion, the aim is to estimate an underlying low-rank matrix from a partial set of binary observations. We propose a novel method for 1-bit matrix completion called Majorization-Minimization Gauss-Newton (MMGN). Our…

We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…